What can I use instead of a ducted range hood in my kitchen?

I know this edges pretty close to a shopping recommendation, but I hope that I’ll manage to stay on the good side. If not, please tell me and I’ll delete the question myself.

My situation: I live in an (older) apartment block have a kitchen without a range hood. I also have no holes in the walls to put the duct into (technically a hole could be drilled, but for various reasons the proper paperwork is nearly impossible to do). There is a ventilation hole, but the local fire safety regulations forbid blocking it (since I have a gas stove/oven), explicitly mentioning that range hoods may not be connected to it. However I could put a fan in it, since that does not block it.

I’ve looked at various recirculating hoods, but they all seem to just filter out some odors and grease (which is nice), but not water vapor (which is not nice). The water vapor actually is a problem occasionally when we do some heavier cooking. I’ve had my kitchen walls slick with moisture on more than one occasion. What I’m surprised about is that I cannot find any hoods with a built-in dehumidifier. Sure, the device would get much heavier and bulkier, and need a connection to the plumbing, but so what? It’d work for me. 😛 Does anyone know if this exists, and if it does, what keywords I should look for?

Barring that, what other options do I have? What kind of device (or combination of devices) would provide the best kitchen exhaust solution while not requiring a dedicated hole in the wall?